T-Test
T-Test — is a method applied for statistical testing of hypotheses. In most situations, the application of the t-test is necessary for checking the equality of the means in two samples. This criterion was developed by William Gosset to evaluate the quality of beer at Guinness company. He was a British statistician. Company management considered the usage of statistical apparatus as the commercial confidentiality which Guinness had to keep. That’s why he published the article under the pseudonym «Student».
What is T-Test
T-test allows the statisticians to compare the means of two groups and, based on the test results, conclude whether they differ statistically from each other or not. T-test may be helpful, if you want to know if the average life expectancy in your region differs from the national average, compare potato yields in different areas, or if your blood pressure changes before and after taking a new drug.
There are several types of t-tests. They differ in the methods and objects of comparison.
There are basic types of t-tests:
- One-sample t-test. This method is utilized to check if the mean value differs from a specific value. Researcher compares the mean value of one group with the assigned value. This assigned value may be any theoretical value (or the mean for a sample).
- Two-sample t-test. This method is utilized to define whether the two mean values of different groups are equal. There are two types of two-sample t-tests.
- Two-sample t-test for independent samples. This method is used to compare the mean values of two different groups.
- Two-sample t-test for dependent samples. This method is used to examine one group at different time intervals or under two different conditions.
There is a range of mathematical assumptions needed to perform a t-test.
- Variances of the two populations should be equal.
- Compared samples should come from normal populations.
- Data should be continuous and ordinal.
- Observations in data should be randomly selected.
- Data should be normally distributed.
- It is necessary to take quite large samples to approximate the data to the normal distribution.
Application of T-Test
In general, the t-test is used in medicine, biology, economics, psychology, mathematics, jurisprudence, and statistics. Currently, it is widely used in programming and data science.
During the testing it is important that the objects of study or analyzed samples were distributed evenly and had at least minimal interaction. They should belong to the same environment and perform the same task. This rule is called the principle of normal distribution. Such a principle is implemented when the studied samples are symmetrical or relatively equivalent, and the average values of the key parameters are approximately the same. Also, the t-test should be performed when the mean values of the samples are identified.
When testing statistical hypotheses, it is essential to adhere to specific rules and use specific methods and tools. Remember that the main hypothesis is initially considered correct until proven otherwise. At the same time, choose the tools and methodology for proving assumptions based on simplicity and convenience.
How to apply the t-test:
- Defining a test object. The researcher should accurately concretize the object of study, define the analyzed elements and formulate the hypothesis to put it forward.
- Data collection. The researcher collects information about the object of study or sample. All materials on which the assessment will be based should be real and reliable. Also, it is important to determine the type of data: theory, quantitative indicators, information, or statistical materials.
- Comparison and assessment. The researcher defines the proper criterion which helps them to identify the presence or absence of the interrelation between studied objects, accepting or declining the hypothesis. Then, the researcher defines the scale of assessment and calculates the necessary indicators and parameters. Mostly, they compare the medium indicators of the process or phenomenon.
- Findings of the study. The researcher should formulate the conclusion based on the data analysis and define whether the hypothesis is valid.
T-test allows us to identify the interrelation between groups of elements, that’s why it is used in various areas. It is applied in psychology and medicine during experiments and observations. The researchers can compare two groups of people with the same disease in different stages. For example, the first group is patients with a primary stroke. The second group is patients with a secondary stroke. Any hypothesis can be put forward: life expectancy after a primary stroke is higher than after a secondary one, or the physical activity of people with a primary disease is better than with a secondary one.
Also, the t-test is widely applied in economics to approve the results of the study. For example, a t-test helps to compare indicators of different years, identify the dynamics and forecast their further development.
